Vagal Nerve Activity and the High Frequency Peak of the Heart Rate Variability

For the Quality of life (QOL) of patients with an artificial heart system, monitoring an information of the cardiovascular control system may be important. We have been evaluating the autonomic nervous system for that purpose. Recently, fluctuations in hemodynamic parameters including heart rate variability (HRV) were evaluated by means of spectral analysis and nonlinear mathematical analysis. Respiratory wavers in HRV were thought ro reflect ongoing information of the parasympathetic nerve activity. Is it true? In order to confirm this hypothesis, we recorded vagal nerve activity directly in the chronic animal experiments. Six healthy adult goats were anesthetized with Halothene inhalation and thoracotomy were performed by the fourth lib resection during mechanical ventilation. Arterial blood pressure, right and left atrial pressures were continuously monitored with the catheter insertion. Cardiac output was measured by the electromagnetic flowmeter attached to the ascending aorta. After the chest was closed, incision was made to the left neck and left vagal nerve was separated. Stainless steel electrodes were inserted into the vagal nerve and fixed by the plasticizer. After the incision was closed, the goats were transferred to the cage and extubated after waking. Hemodynamic parameters and vagal nerve activity were measured in the awake condition. The results showed that clear observation of the autonomic nerve discharges were embodied by this experimental system. The vagal nerve discharges were synchronized with heart beat and respiration. The vagal nerve tonus was significantly influenced by the hemodynamic alteration. However in some condition, the respiratory wave was not always consistent with tonus of the vagal nerve activity, thus suggesting that we should check another information to evaluate the parasympathetic tone. We must continue this study to evaluate an autonomic nerve during artifical heart circulation.

Monitoring System for the Totally Implantable Ventricular Assist System by Use of Sensors for Virtual Reality

For the development of the totally implantable artificial organs, it is an important problem to monitor the conditions of the implantable devices, especially when used in clinical cases. In this study, we used position sensors for the 3-dimensional (3-D) virtual reality (VR) system monitor an implantable artificial heart. The sensors used in the experiments were 3-space Fastrak (Polhemus, USA). The position sensors using electro-magnetic forces were attached to the inner actuating zone. Sensitivity of the position sensors was in the order of around 0.8 mm. By use of these VR position sensors, we could easily detect the six degrees of freedom as x,y,z, and pitch, yaw, roll of these sensors. Experimental evaluation using a model circulation loop and healthy adult goats was performed. Experimental results suggest that our newly developed implantable sensors for monitoring the implantable artificial heart system were useful for sensing driving condition, thus possibly useful for the implantable devices for clinical usage.

Development of Total Artificial Heart with Economical and Durability Advantages

To develop a total artificial heart (TAH) pump system, we created a design paying particular attention to durability and cost. We adopted a pneumatically driven sac type artificial heart, where the configuration of the sac was decided according to the methodology of flow visualization. Its configuration is almost round to achieve as little stagnation as possible and a low turbulent flow. The main body of the sac was made using polyvinyl chloride (PVC) paste. The paste was poured into an external mold, and heated in a hot air drying oven. Coating was performed using polyurethane. The basic performance of this pump system was tested using a model circulation circuit, and a fitting study through acute animal experiment, using a healthy adult goat, was carried out. As for the TAH produced experimentally, a pump output exceeding 5.0 l/min in the model circulation circuit was provided. Implantation in the internal pleural cavity of a healthy adult goat, 55 kg in weight, proved possible and quite easy in comparison. It is thought that a more refined design in the connector part is desirable. Furthermore, a chronic experiment with the TAH will be carried out, and examination will need to be repeated in the future.

Can the Artificial Heart Make the Circulation Become Fractal?

In order to analyze the hemodynamic parameters in prosthetic circulation as an entity and not as decomposed parts, non linear mathematical analyzing techniques, including the fractal dimension analyzing theory, were utilized. Two pneumatically actuated ventricular assist devices were implanted, as biventricular bypasses (BVB), in chronic animal experiments, using four healthy adult goats. For the comparison between the natural and prosthetic circulation in the same animals, the BVB type complete prosthetic circulation model with ventricular fibrillation, was adopted. All hemodynamic parameters with natural and prosthetic circulation were recorded under awake conditions, and calculated with a personal computer system. Using the non-linear mathematical technique, the arterial blood pressure waveform was embedded into the return map as the beat-to-beat time series data and fractal dimension analysis were performed to analyze the reconstructed attractor. By the use of the Box counting method, fractal dimension analysis of the hemodynamics was performed. Return map of the hemodynamics during natural and artificial circulation showed fractal characteristics, and fractal dimension analysis of the arterial blood pressure revealed the fact that lower dimensional fractal dynamics were evident during prosthetic circulation. Fractal time series data is suggested to have robustness and error resistance, thus our results suggest that the circulatory regulatory system with an artificial heart may have these desired characteristics.

Detection of the cardiac function by fractal dimension analysis

Nonlinearity in circulation control attracts attention because nonlinearity is thought to be essential in the function of the living body. Many investigators have pointed out that the analysis of heart rate variability in particular is important in the analysis of autonomic nerve and cardiac function evaluation. Heart rate variability shows nonlinear behavior. However, until the present, many reports have been premised on linearity; linear correlation by frequency analysis has been used by many studies. However, in terms of this methodology, there is a problem applying it to the nonlinear living body. Therefore, fractal and chaos methodology has been used. The ascertainment of cardiac function has become important in allowing the clinical stage of a ventricular assist system to be successful. The purpose of this study was cardiac function evaluation by a methodology that was premised on nonlinearity. Chaos and fractal theory was used as a nonlinear dynamic theory. As a methodology of measurement, the volume of the left ventricle was used rather than an electrocardiogram, the waveform of arterial blood pressure. The volume was measured using acoustic quantification (AQ) ultrasonic echocardiography. Using these methodologies, the time series of many patients were analyzed. For example, drug administration was attempted in this study, and it was found that some drugs like ACE inhibitors showed a significant effect upon nonlinear dynamics in the cardiovascular system. The result, which attempted cardiac function evaluation by these various methodologies, is reported.

Peripheral vascular resistances during total left heart bypass with an oscillated blood flow

For development aimed at a totally implantable type ventricular assist device (VAD), the vibrating flow pump (VFP) has been developed at Tohoku University. A transcutaneous energy transmission system (TETS) using amorphous fibers was developed to power the totally implantable VAD system. The VFP works at a high frequency compared to that of a natural heart of a biological system. It is a frequency of 10-50 Hz. In this research, animal experiments with left heart bypass were carried out with healthy adult goats. For comparison between nonpulsatile flow and oscillated flow, a rotary pump (RP) and the VFP were used in the experiments. For the achievement of total left heart bypass, left ventricular approaches were carried out, and blood was pumped from the left ventricle to the descending aorta. Adequate support of the left heart was provided by both pumps. In terms of the results, the vascular resistances tended to decrease during the use of both pumps during 100% bypass driving. When we compared these pumps at the same flow rate, the resistances during RP driving were significantly smaller than those during VFP driving. These results may suggest that the influences of the VFP upon the peripheral vessels may be relatively small compared to those of the RP. This may be an important result when a stable hemodynamic condition is required during artificial circulation. The VFP was considered as a candidate for a totally implantable VAD as a result.

Vagal nerve activity recording in the awake condition for the control of an artificial heart system

To detect useful information for an artificial heart control system, we paid attention to the autonomic nervous system. For stable recording, we used vagal nerve activity in chronic animal experiments using healthy adult goats in an awake condition because this nerve was sufficiently bold and large enough. Vagal nerve discharges were successfully recorded from awake goats. They were synchronized with respiration and responded to the hemodynamic changes induced by drug administration, suggesting that they may provide useful information for an artificial heart control algorithm. For automatic control, some time delay plays a vitally important role. Thus, predictive control for an artificial heart system may be desirable. It may be embodied by the use of autonomic nerve information.

Vagal nerve activity and the high frequency peak of the heart rate variability

For the Quality of life (QOL) of patients with an artificial heart system, monitoring an information of the cardiovascular control system may be important. We have been evaluating the autonomic nervous system for that purpose. Recently, fluctuations in hemodynamic parameters including heart rate variability (HRV) were evaluated by means of spectral analysis and nonlinear mathematical analysis. Respiratory wavers in HRV were thought to reflect ongoing information of the parasympathetic nerve activity. Is it true? In order to confirm this hypothesis, we recorded vagal nerve activity directly in the chronic animal experiments. Six healthy adult goats were anesthetized with Halothene inhalation and thoracotomy were performed by the fourth lib resection during mechanical ventilation. Arterial blood pressure, right and left atrial pressures were continuously monitored with the catheter insertion. Cardiac output was measured by the electromagnetic flowmeter attached to the ascending aorta. After the chest was closed, incision was made to the left neck and left vagal nerve was separated. Stainless steel electrodes were inserted into the vagal nerve and fixed by the plasticizer. After the incision was closed, the goats were transferred to the cage and extubated after waking. Hemodynamic parameters and vagal nerve activity were measured in the awake condition. The results showed that clear observation of the autonomic nerve discharges were embodied by this experimental system. The vagal nerve discharges were synchronized with heart beat and respiration. The vagal nerve tonus was significantly influenced by the hemodynamic alteration. However in some condition, the respiratory wave was not always consistent with tonus of the vagal nerve activity, thus suggesting that we should check another information to evaluate the parasympathetic tone. We must continue this study to evaluate an autonomic nerve during artificial heart circulation.

Origin of chaos in the circulation: open loop analysis with an artificial heart

To develop the optimal automatic control algorithm for an in vivo artificial heart system, investigation of the basic characteristics of the cardiovascular system may be important. The clinical significance of chaotic dynamics in the cardiovascular system has attracted attention. The circulation is a so-called complex system with many feedback circuits, making it very difficult to investigate the origin of chaos within the system. In this study, we investigated the origin of chaos by open loop analysis with an artificial heart (which has no fluctuation in pumping rate or contraction power) in chronic animal experiments with healthy adult goats. As a result, in the artificial heart circulatory time series data, low dimensional deterministic chaos was discovered by nonlinear mathematical analysis, suggesting the importance of blood vessels in the chaotic dynamics of the cardiovascular system. To investigate the origin of chaos further, sympathetic activity was directly measured in animals with artificial hearts. Chaotic dynamics was also recognized in sympathetic action potentials, even during artificial heart circulation. Coupling of the nonlinear information between blood vessels and sympathetic activity was suggested by analysis of mutual information. In chaotic dynamics, the central nervous system (CNS) played an important role through sympathetic activity. These findings may be useful for the development of an automatic control algorithm for an artificial heart.

Monitoring system for the totally implantable ventricular assist system by use of sensors for virtual reality

For the development of the totally implantable artificial organs, it is an important problem to monitor the conditions of the implantable devices, especially when used in clinical cases. In this study we used position sensors for the 3-dimensional (3-D) virtual reality (VR) system monitor an implantable artificial heart. The sensors used in the experiments were 3-space Fastrak (Polhemus, USA). The position sensors using electro-magnetic forces were attached to the inner actuating zone. Sensitivity of the position sensors was in the order of around 0.8 mm. By use of these VR position sensors, we could easily detect the six degrees of freedom as x,y,z, and pitch, yaw, roll of these sensors. Experimental evaluation using a model circulation loop and healthy adult goats was performed. Experimental results suggest that our newly developed implantable sensors for monitoring the implantable artificial heart system were useful for sensing driving condition, thus possibly useful for the implantable devices for clinical usage.

Control of the pulmonary arterial resistance by the use of the oscillated assist flow

In the clinical application of supporting circulation, the treatment of a patient with pulmonary hypertension is very important. We developed the electromagnetically driven vibrating flow pump (VFP) as a totally implantable type ventricular assist system. The artificial heart driven by electromagnetic forces creates high speed oscillation flow around 10-50 Hz. Assistance by high-speed oscillation flow has an interesting influence on the cardiovascular system. In this study, we carried out research on the influence such oscillation flow had on the pulmonary arterial vessels, and the supporting flow wave-form that controlled pulmonary vascular resistance was considered. Six healthy adult goats of both sexes were used in the experiments. We carried out inhalation anesthesia and performed intubation. The thorax was opened through left fourth rib resection. Right heart bypass was performed from the right atrium to the pulmonary artery. The flow of right heart assistance was maintained within 20-25% of total flow. Our purpose was to add flow of a specific high frequency to the right heart circulation. The hemodynamic parameters were recorded on a magnetic tape data recorder and input into a computer through an A-D converter. A result identified was that the pulmonary vascular resistance changed according to the alteration of the driving frequency of the VFP even during the same flow assistance. The resistance of the pulmonary arterial vessels became smaller when the driving of the VFP of 30 Hz was added to the right heart circulation. This was significant even when compared with continuous flow right heart assist. The characteristics of impedance appeared to have interesting alterations as well. Control of pulmonary vascular resistance by right heart assistance becomes possible if these results are applied. Accordingly, it may become one of the choices for treatment of a patient with pulmonary hypertension.

Development of total artificial heart with economical and durability advantages

To develop a total artificial heart (TAH) pump system, we created a design paying particular attention to durability and cost. We adopted a pneumatically driven sac type artificial heart, where the configuration of the sac was decided according to the methodology of flow visualization. Its configuration is almost round to achieve as little stagnation as possible and a low turbulent flow. The main body of the sac was made using polyvinyl chloride (PVC) paste. The paste was poured into an external mold, and heated in a hot air drying oven. Coating was performed using polyurethane. The basic performance of this pump system was tested using a model circulation circuit, and a fitting study through acute animal experiment, using a healthy adult goat, was carried out. As for the TAH produced experimentally, a pump output exceeding 5.0 l/min in the model circulation circuit was provided. Implantation in the internal pleural cavity of a healthy adult goat, 55 kg in weight, proved possible and quite easy in comparison. It is thought that a more refined design in the connector part is desirable. Furthermore, a chronic experiment with the TAH will be carried out, and examination will need to be repeated in the future.

Left heart bypass using the oscillated blood flow with totally implantable vibrating flow pump

Aiming at a totally implantable ventricular assist device (VAD), a vibrating flow pump (VFP) was developed in Tohoku University. A transcutaneous energy transmission system (TETS) using an amorphous fiber was developed for the totally implantable VAD system. The VFP works with a higher frequency than the natural heart of a biological system, a frequency of 10-50 Hz. In this research, animal experiments on left heart bypass were performed with healthy goats. Blood from the apex of the left ventricle was received and was sent to the aorta so that an adequate supporting effect of the left heart was provided. In particular, the depression effect of the left ventricle was obvious. As a result, sufficient artificial heart flow was provided. For a totally implantable type VAD, left heart bypass of almost 100% may become necessary in some situations. Therefore, apex approaches of left heart bypass may be desirable. From an anatomical consideration, an apex of the heart is suitable for the VFP of this totally implantable type. In the left heart bypass for which the apex of the heart was used, an almost 100% bypass was possible. This is a requirement that is important when waiting for recovery of sufficient cardiac function. It is also important that left heart circulation is maintained fully by an artificial heart of the complete implantation type. The VFP was considered to be useful as a totally implantable type artificial heart from the results.

Pulmonary arterial impedance analysis by the use of the oscillated assist flow

Pulmonary arterial impedance is an important and interesting characteristic that can be used to evaluate the physiological properties of the pulmonary vessel. However, power spectrum analysis of the pulmonary artery pressure and flow pattern have suggested that peak power in the relatively high frequency range (> 10 Hz) is significantly low; thus, we cannot analyze the vessel properties in the high frequency range. In this study, we used the newly developed vibrating flow pump (VFP), which can generate oscillated blood flow with a relatively high frequency (10-50 Hz) for right heart bypass, to evaluate the pulmonary arterial impedance pattern in the high frequency range. Acute animal experiments of the right heart bypass from the right atrium to the pulmonary artery using 6 healthy adult goats were performed. The flow pattern and pressure of the pulmonary artery, electrocardiograms (ECGs), and arterial and right atrial pressures were continuously monitored during the experiments. Spectral analysis of the hemodynamic parameters using the fast Fourier transform (FFT) method was performed to evaluate the spectral properties. The coherence function, transfer function, and phase patterns were calculated to analyze the impedance pattern in the relatively high frequency area. Previously, various investigators had tried to analyze the impedance patterns of the pulmonary artery; however, they could not analyze the impedance patterns over 10 Hz because the spectral patterns of the pulmonary flow do not have high power at high frequencies. These physiological analyses may be useful in designing the optimal pulmonary circulation.

Nonlinear mathematical analysis of the hemodynamic parameters during left ventricular assistance with oscillated blood flow

For the development of a totally implantable ventricular assist system (VAS), we have been developing the vibrating flow pump (VFP), which can generate oscillated blood flow with a relatively high frequency (10-50 Hz) for a totally implantable system. In this study, effects of left ventricular assistance with this unique oscillated blood flow were analyzed by nonlinear mathematics for evaluation as the entire circulatory regulatory system, not as a separate part of the system. Left heart bypasses using VFPs from the left atriums to the descending aortas were performed in chronic animal experiments using healthy adult goats. Electrocardiogram (ECG), arterial blood pressure, VFP pump flow, and flow of the descending aorta data taken while the goats were awake were recorded in the data recorder and analyzed in the personal computer system through the AD convertor. Using nonlinear mathematics, time series data were embedded into the phase space, and the Lyapunov numerical method, fractal dimension analysis, and power spectrum analysis were performed to evaluate the nonlinear dynamics. During left ventricular assistance with the VFP, Mayer wave fluctuations were decreased in the power spectrum, the fractal dimension of the hemodynamics was significantly decreased, and peripheral vascular resistance was significantly decreased. These results suggest that nonlinear dynamics, which mediate the cardiovascular dynamics, may be affected during LV bypass with oscillated flow. Decreased power of the Mayer wave in the spectrum caused the limit cycle attractor of the hemodynamics and decreased the peripheral resistance. Decreased sympathetic discharges may be the origin of the decreased Mayer wave and fractal dimension. These nonlinear dynamical analyses may be useful to design the optimal VAS control.

Extracting 1/f fluctuation from the arterial blood pressure of an artificial heart

We have studied the fluctuations of an artificial circulation for the analysis of the physiological aspects; however, the conventionally used fast Fourier transform (FFT) method cannot separate harmonic oscillations, such as respiratory and Mayer waves, from the 1/f fluctuation, which has been though to represent underlying fractal dynamics. Fractal structure was shown in the strange attractor with chaotic dynamics, which is thought to be a flexible and intelligent system. In this study, the coarse-graining spectral analyzing (CGSA) method was utilized to quantitatively evaluate the proportion of the 1/f fluctuation in the total power in the frequency domain and to analyze artificial circulation in the whole system. We implanted two pneumatically actuated ventricular assist devices as biventricular bypasses (BVBs) in chronic animal experiments using 4 healthy adult goats. To compare the natural and prosthetic circulation of each experimental animal, the BVB-type complete prosthetic circulation model with electrically induced ventricular fibrillation was adopted. All hemodynamic parameters of natural and prosthetic circulation were recorded under awake conditions and calculated with the use of a personal computer. With the use of the CGSA method, time-series data of the hemodynamics were analyzed and fractal percentages, extracting the 1/f fluctuation from a given time series, were calculated. Fractal percentages of the arterial blood pressure were 85.8 +/- 10.7% and 82.0 +/- 7.3% with natural and artificial circulation, respectively (not significant [NS]). 1/f fluctuation showed the characteristics of being fractal in a time series. The fractal structure showed robustness and error resistance in nonlinear dynamics. Therefore, our results suggest that the circulatory regulatory system of the artificial heart may have desirable characteristics such as error resistance.

Fluctuations of the hemodynamic derivatives during left ventricular assistance using oscillated blood flow

To analyze the autonomic nervous system during left heart bypass with a vibrating flow pump (VFP), fluctuations in hemodynamic derivatives were evaluated by the spectral analysis method using fast fourier transform methodology. After the left pleural cavity was opened through the fourth intercostal space under general anesthesia, a VFP was implanted as the left heart bypass device in chronic animal experiments using 3 healthy adult goats. Hemodynamic parameters with and without VFP assistance were recorded on magnetic tape in awake animals and were analyzed by computer through an analog to digital convertor. Power spectral analysis was performed on a beat-to-beat basis for the evaluation of the fluctuations. During left heart bypass with the VFP, Mayer wave fluctuations were decreased significantly although respiratory waves were not changed significantly. These results suggest that sympathetic nervous system modulation was changed under the influences of the left heart bypass with VFP. By using this analysis methodology, truly physiologic ventricular assistance may be achieved.

Spectral analysis of hemodynamics during left ventricular assistance

In order to analyze the autonomic nervous system during left ventricular (LV) assistance, fluctuations in hemodynamic derivatives were evaluated by a spectral analyzing method using a fast fourier transform (FFT) methodology. After the left pleural cavity was opened through the fourth intercostal space under general anesthesia, a pneumatically driven ventricular assist system was implanted as in left heart bypasses in chronic animal experiments, using three healthy adult goats. Hemodynamic parameters with and without LV assistance were recorded on a magnetic tape in the awake condition then analyzed in a computer system through an A-D convertor. Power spectral analysis was performed on a beat-to-beat basis for the evaluation of the fluctuations. During copulsation mode LV assistance, Mayer wave fluctuations (0.1 Hz) were significantly increased compared with counterpulsation mode LV assist, suggesting an increase in sympathetic tone. Co-pulsation mode LV assist is reported to increase the afterload of the natural left ventricle, thus, the sympathetic tone may be increased to maintain a natural heart output.

Fractal dimension analysis of the oscillated blood flow with a vibrating flow pump

To analyze the hemodynamic parameters during circulation with oscillated blood flow, nonlinear mathematical analyzing techniques, including fractal theory, were utilized. Vibrating flow pumps (VFP) were implanted as a left heart bypass, and the ascending aorta was clamped to constitute the total left heart circulation with oscillated blood flow in acute animal experiments using 7 adult goats. Using nonlinear mathematical analyzing techniques, reconstructed attractors of the arterial blood pressure waveform in the phase space during natural circulation and oscillated circulation were analyzed. Using the Grassberger-Procaccia correlation dimension analyzing technique, fractal dimension analysis of the reconstructed attractor was performed. During VFP bypass, lower fractal dimensions of the reconstructed attractor were shown compared with those during natural heart circulation. The results suggest that lower dimensional chaotic dynamics contributed to the circulation with oscillated blood flow.

Can the artificial heart make the circulation become fractal?

In order to analyze the hemodynamic parameters in prosthetic circulation as an entity and not as decomposed parts, non linear mathematical analyzing techniques, including the fractal dimension analyzing theory, were utilized. Two pneumatically actuated ventricular assist devices were implanted, as biventricular bypasses (BVB), in chronic animal experiments, using four healthy adult goats. For the comparison between the natural and prosthetic circulation in the same animals, the BVB type complete prosthetic circulation model with ventricular fibrillation, was adopted. All hemodynamic parameters with natural and prosthetic circulation were recorded under awake conditions, and calculated with a personal computer system. Using the non-linear mathematical technique, the arterial blood pressure waveform was embedded into the return map as the beat-to-beat time series data and fractal dimension analysis were performed to analyze the reconstructed attractor. By the use of the Box counting method, fractal dimension analysis of the hemodynamics was performed. Return map of the hemodynamics during natural and artificial circulation showed fractal characteristics, and fractal dimension analysis of the arterial blood pressure revealed the fact that lower dimensional fractal dynamics were evident during prosthetic circulation. Fractal time series data is suggested to have robustness and error resistance, thus our results suggest that the circulatory regulatory system with an artificial heart may have these desired characteristics.

Deterministic chaos in the hemodynamics of an artificial heart

To analyze the hemodynamic parameters during prosthetic circulation as an entity, non linear mathematical techniques were used. To compare natural and prosthetic circulation, two pneumatically actuated ventricular assist devices were implanted as biventricular bypasses in chronic animal experiments using adult goats to consitute the biventricular bypass complete prosthetic circulation model with ventricular fibrillation. After implantation, these goats were placed in a cage and extubated after waking. All hemodynamic parameters with the natural circulation without biventricular bypass pumping, and the artificial circulation with biventricular bypass pumping under ventricular fibrillation were recorded under awake conditions. By the use of a non linear mathematical technique, the arterial blood pressure waveform was embedded into a four dimensional phase space and projected into three dimensional phase space. The Lyapunov numeric method is used as an adjunct to the graphic analysis of the state space. A phase portrait of the attractor showed a high dimension complex structure, with three dimensional solid torus suggesting deterministic chaos during natural circulation. However, a simple attractor, such as a limit cycle attractor, was observed during artificial circulation. Positive Lyapunov exponents during artificial circulation suggest the lower dimensional chaotic system. Thus, hemodynamic parameters during prosthetic circulation must be carefully controlled when unexpected stimuli are fed from outside.

Chaotic behavior of hemodynamics with ventricular assist system

In order to analyze hemodynamic parameters during left ventricular assistance as an entity and not as decomposed parts, non-linear mathematical techniques were utilized. Pneumatically actuated ventricular assist systems (VAS) were implanted as left heart bypasses in acute animal experiments, using healthy adult mongrel dogs. By the use of the non-linear mathematical technique, the arterial blood pressure waveform (AP) was embedded into the four-dimensional phase space and projected into the three-dimensional phase space. The Lyapunov numerical method was used as an adjunct to the graphical analysis of the state space. The phase portrait of the attractor showed a complex structure; a three dimensional solid torus with a screw type structure as a part, suggesting deterministic chaos in the AP without left ventricular assistance. Positive lyapunov exponents confirmed the existence of chaos. During counterpulsation mode left ventricular assistance, the phase portrait of the attractor showed a more complex structure, and positive Lyapunov exponents suggested a greater dimensional deterministic chaos. However, non-structured patterns were seen in the phase space during internal mode VAS driving, suggesting the possibility of dissipative dynamics in the four dimensional phase space. These results suggest that the cardiovascular system with counterpulsation mode VAS driving is in a homeochaotic state, which is thought to be a flexible and intelligent control system. And there is greater dimensional complex dynamics in the circulatory regulatory system with VAD during internal mode assistance.

Origin of the rhythmical fluctuations in the animal without a natural heartbeat

In order to analyze the origin of the rhythmical fluctuations in the cardiovascular system, an artificial heart, which does not have rhythmical periodicities such as altering heart rate and cardiac function, was utilized in chronic animal experiments with adult goats. Two pneumatically actuated ventricular assist devices were implanted as a total biventricular bypass under general anesthesia, and then the natural heart was electrically fibrillated to constitute the biventricular bypass type of complete prosthetic circulation model. All hemodynamic data were recorded under awake conditions and were calculated in the computer system by spectral analysis methods. In the power spectrum of the arterial blood pressure of the animal with the artificial heart, the Mayer wave peak and respiratory wave peak were clearly observed, and spectral analysis including the coherence function suggests that the Mayer waves originated from the peripheral vascular resistance and the respiratory waves probably originated from the periodicities of the pulmonary circulation. These fluctuations in the circulatory system influenced the arterial baroreflex system and transfer to the sympathetic outflow through the central baroreflex system, which suggests that rhythmical fluctuations in hemodynamic parameters originate at least in part from these vascular periodicities.